Stochastic parameterization: uncertainties from convection

In 2005, the ECMWF held a workshop on stochastic parameterisation, at which the convection was seen as being a key issue. That much is clear from the working group reports and particularly the statement from working group 1 that “it is clear that a stochastic convection scheme is desirable”. The present note aims to consider our current status in comparison with some of the issues raised and hopes expressed in that working group report

Levy-funded research choices by producers and society

Commodity levies are used increasingly to fund producer collective goods such as research and promotion. In the present paper we examine theoretical relationships between producer and national benefits from levy‐funded research, and consider the implications for the appropriate rates of matching government grants, applied with a view to achieving a closer match between producer and national interests. In many cases the producer and national optima coincide. First, regardless of the form of the supply shift, when product demand is perfectly elastic, or all the product is exported, domestic benefits and costs of levy‐funded research all go to producers and they have appropriate incentives. Second, if research causes a parallel supply shift, the producer share of research benefits is the same as their share of costs of a levy, and their incentives are compatible with national interests. In such cases, a matching grant would cause an over‐investment in research from a national perspective. However, if demand is less than perfectly elastic, and research causes a pivotal supply shift, the producer share of benefits is smaller than their share of costs of the levy, and they will under‐invest in research from a national point of view. A matching grant can be justified in such cases, however the magnitude of the optimal grant is sensitive to market conditions.Research and Development/Tech Change/Emerging Technologies,

Resonance fluorescence in a band gap material: Direct numerical simulation of non-Markovian evolution

A numerical method of calculating the non-Markovian evolution of a driven atom radiating into a structured continuum is developed. The formal solution for the atomic reduced density matrix is written as a Markovian algorithm by introducing a set of additional, virtual density matrices which follow, to the level of approximation of the algorithm, all the possible trajectories of the photons in the electromagnetic field. The technique is perturbative in the sense that more virtual density matrices are required as the product of the effective memory time and the effective coupling strength become larger. The number of density matrices required is given by $3^{M}$ where $M$ is the number of timesteps per memory time. The technique is applied to the problem of a driven two-level atom radiating close to a photonic band gap and the steady-state correlation function of the atom is calculated.Comment: 14 pages, 9 figure

Spinor fields without Lorentz frames in curved spacetime using complexified quaternions

Using complexified quaternions, a formalism without Lorentz frames, and therefore also without vierbeins, for dealing with tensor and spinor fields in curved spacetime is presented. A local U(1) gauge symmetry, which, it is speculated, might be related to electromagnetism, emerges naturally.Comment: 14 pages; v2: minor corrections; v3: note added concerning unified treatment of local Lorentz transformations and local U(1) gauge transformations; v4: published in J. Math. Phys. 50 083507 (2009